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            <h1 style="display: none">CF1516B.二进制</h1>
            
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              <h1 id="位运算（异或）CFR717DIv-21516B-AGAGA-XOOORRR"><a href="#位运算（异或）CFR717DIv-21516B-AGAGA-XOOORRR" class="headerlink" title="位运算（异或）CFR717DIv.21516B. AGAGA XOOORRR"></a>位运算（异或）<a target="_blank" rel="noopener" href="https://codeforces.com/contest/1516/problem/B">CFR717DIv.21516B. AGAGA XOOORRR</a></h1><p>这里考查异或的性质：</p>
<h2 id="x-y-z-lt-—–-gt-y-x-z"><a href="#x-y-z-lt-—–-gt-y-x-z" class="headerlink" title="x^y==z&lt;—–&gt;y==x^z"></a>x^y==z&lt;—–&gt;y==x^z</h2><h2 id="x-x-0"><a href="#x-x-0" class="headerlink" title="x^x=0"></a>x^x=0</h2><h2 id="题意："><a href="#题意：" class="headerlink" title="题意："></a>题意：</h2><p>t组，每组n和n个数，现在可以选任意两个相邻的数取异或，其结果取代原本两个数。问是否可以通过若干次操作使之只剩下两个以上个相同的数。</p>
<h2 id="题解："><a href="#题解：" class="headerlink" title="题解："></a>题解：</h2><p>首先考虑剩下几个数。</p>
<h3 id="剩下两个："><a href="#剩下两个：" class="headerlink" title="剩下两个："></a>剩下两个：</h3><p>上述提到的，x^x=0，所以若所有数^起来的结果为0，那么说明可以分成两个相同的数。</p>
<h3 id="剩下三个："><a href="#剩下三个：" class="headerlink" title="剩下三个："></a>剩下三个：</h3><p>设分别为a，b，c。</p>
<p>那么应该有a==b==c。</p>
<p>我们由上述知道：x^y==z&lt;—–&gt;x==y^z</p>
<p>取一下异或前缀s[n]，设a=s[i]，b=s[j]，c=b[n]。则应该有：</p>
<figure class="highlight stylus"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><code class="hljs stylus">s<span class="hljs-selector-attr">[i]</span>==s<span class="hljs-selector-attr">[i]</span>^s<span class="hljs-selector-attr">[j]</span><span class="hljs-comment">//a==b</span><br>s<span class="hljs-selector-attr">[i]</span>==s<span class="hljs-selector-attr">[j]</span>^s<span class="hljs-selector-attr">[n]</span><span class="hljs-comment">//a==c</span><br></code></pre></td></tr></table></figure>

<h3 id="剩下m（m-gt-3）个："><a href="#剩下m（m-gt-3）个：" class="headerlink" title="剩下m（m&gt;3）个："></a>剩下m（m&gt;3）个：</h3><p>分成4个以上都可以转化为2个或3个，如下：</p>
<h4 id="转化为两个："><a href="#转化为两个：" class="headerlink" title="转化为两个："></a>转化为两个：</h4><p>比如4个：a==b==c==d，那么可以做操作：a==b  (c^d)</p>
<p>这里c==d所以c^d==0，</p>
<p>又x^0==x，</p>
<p>所以分成了：a   b    0</p>
<p>这里a^b==a^b^0，即ans==a^b^0==a^b。</p>
<p>那么就转化为两个了。</p>
<h4 id="转化为三个"><a href="#转化为三个" class="headerlink" title="转化为三个"></a>转化为三个</h4><p>比如五个：a==b==c==d==e，同样可以做操作：a==b==c  d^e</p>
<p>即：a==b==c 0</p>
<p>即：a==b==c</p>
<p>那么就转化为三个了。</p>
<p>所以本质上只有两个和三个的情况，那么问题就解决了。</p>
<h2 id="贴代码："><a href="#贴代码：" class="headerlink" title="贴代码："></a>贴代码：</h2><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br></pre></td><td class="code"><pre><code class="hljs c++">        <span class="hljs-comment">// violet apricity</span><br>        <span class="hljs-comment">// Do all I can do.Do good to be good.</span><br><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;iostream&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;stdio.h&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;cstring&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;string&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;algorithm&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;vector&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;math.h&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;map&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;sstream&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;numeric&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string">&lt;queue&gt;</span></span><br><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> STD using namespace std;</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> ll long long</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> db double</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> ldb long double</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> IOS std::ios::sync_with_stdio(false),std::cin.tie(0),std::cout.tie(0);</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> MAX 88888888</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> INF 0x3f</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> r0 return 0;</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> SYP system(<span class="hljs-meta-string">&quot;pause&quot;</span>);</span><br><span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> endl <span class="hljs-meta-string">&#x27;\n&#x27;</span></span><br><br>STD<br><span class="hljs-keyword">int</span> a[<span class="hljs-number">2020</span>],b[<span class="hljs-number">2020</span>];<br><span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span></span><br><span class="hljs-function"></span>&#123;<br>    <span class="hljs-comment">//IOS</span><br>    <span class="hljs-keyword">int</span> t;cin&gt;&gt;t;<br>    <span class="hljs-keyword">while</span>(t--)&#123;<br>        <span class="hljs-keyword">int</span> n;cin&gt;&gt;n;<br>        <span class="hljs-keyword">int</span> ans=<span class="hljs-number">0</span>;<br>        <span class="hljs-keyword">for</span>(<span class="hljs-keyword">int</span> i=<span class="hljs-number">1</span>;i&lt;=n;i++)&#123;<br>            cin&gt;&gt;a[i];<br>            ans^=a[i];<br>            b[i]=b[i<span class="hljs-number">-1</span>]^a[i];<br>        &#125;<br>        <span class="hljs-keyword">bool</span> yes=<span class="hljs-number">0</span>;<br>        <span class="hljs-keyword">if</span>(ans==<span class="hljs-number">0</span>)&#123;cout&lt;&lt;<span class="hljs-string">&quot;YES\n&quot;</span>;<span class="hljs-keyword">continue</span>;&#125;<br>        <span class="hljs-keyword">for</span>(<span class="hljs-keyword">int</span> i=<span class="hljs-number">1</span>;i&lt;=n;i++)&#123;<br>            <span class="hljs-keyword">for</span>(<span class="hljs-keyword">int</span> j=i+<span class="hljs-number">1</span>;j&lt;=n;j++)&#123;<br>                <span class="hljs-keyword">if</span>(b[i]==(b[i]^b[j])&amp;&amp;b[i]==(b[j]^b[n]))&#123;<br>                    yes=<span class="hljs-number">1</span>;<span class="hljs-keyword">break</span>;<br>                &#125;<br>            &#125;<br>            <span class="hljs-keyword">if</span>(yes==<span class="hljs-number">1</span>)<span class="hljs-keyword">break</span>;<br>        &#125;<br>        <span class="hljs-keyword">if</span>(yes)cout&lt;&lt;<span class="hljs-string">&quot;YES\n&quot;</span>;<br>        <span class="hljs-keyword">else</span> cout&lt;&lt;<span class="hljs-string">&quot;NO\n&quot;</span>;<br>    &#125;<br>    SYP<br>    r0<br>&#125;<br></code></pre></td></tr></table></figure>
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        searchFunc(path, 'local-search-input', 'local-search-result');
      });
      $('#modalSearch').on('shown.bs.modal', function() {
        $('#local-search-input').focus();
      });
    })()
  </script>















<!-- 主题的启动项 保持在最底部 -->
<script  src="/js/boot.js" ></script>


</body>
</html>
